Category UNSTEADY AERODYNAMICS, AEROACOUSTICS AND AEROELASTICITY OF TURBOMACHINES

Yang, D. B. Sims-Williams, and L. He

School of Engineering, University of Durham, Durham, DH1 3LE, U. K.

Abstract A method of correcting distortion in measured unsteady pressures using a tubing system and off-board pressure transducers is described. This technique involves the frequency domain correction using the known tubing transfer function and not only corrects the amplitude distortion, but also eliminates the phase shift. The technique is demonstrated for surface pressures in a turbomachinery blade flitter case, and for wake measurements for a vortex shedding case.

1. Introduction

In recent years, computational methods for predicting unsteady few through turbomachines have been fully developed. For the validation of these codes, systematic, accurate, and detailed unsteady pressure experimental data are needed. Most previous measurements are confined to the use of miniature high-response pressure transducers buried in the blade surface (largely on 2D sections) of linear oscillating cascades (Buffum 1993, Carta 1978 and Fleeter, 1977), annular cascades (Bolcs and Korbacher, 1993, Fransson 1990) and ro­tating machines (Manwaring 1997, Frey 2001, Minkiewicz 1998). Due to the transducer size limitation and airfoil contour preservation as well as expensive cost, only a limited number of unsteady signals can be obtained. Unsteady (static and stagnation) pressure field patterns are not obtained; these could be used to improve understanding of the few, to identify modeling limitations, and to aid future development for both aeromechanic and aerothermal (e. g. unsteady loss) applications. With embedded transducers, the movement of the blade subjects the transducer to an acceleration, for which an extensive calibra­tion and correction is required. Various installation configurations have been designed to isolate the miniature pressure transducers from the airfoil strain and centrifugal loads to improve the durability. Improved transducer charac­teristics are desired to diminish temperature sensitivity. In order to provide the required spatial resolution of the unsteady few measurements at blade sur-

521

K. C. Hall et al. (eds.),

Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 521-529. © 2006 Springer. Printed in the Netherlands.

faces, various optical measurement techniques (pressure sensitive paints – PSP, doppler sensors, micromachined fabry-perot pressure sensors and so on) were developed. However, every method requires a complicated optical technique and expensive equipment. These issues can be avoided by using off-board pressure transducers. The blade can be instrumented by detailed static pres­sure tappings, which are connected to the off-board pressure transducer by the pneumatic tubing. This approach makes economical use of pressure transduc­ers. However, the tubing system, characterized by the tubing length, its internal diameter, and the transducer internal volume, introduces a distortion of the un­steady signals. In the area of turbomachinery aeroelasticity, this distortion of the unsteady signal was generally either neglected because of low frequencies and short tubing lengths (He & Denton, 1991), or it simply was corrected for phase lag and amplitude attenuation for a certain tubing length (Bell and He, 2000). In the present work, a correction method is used which is more gen­erally applicable in that it corrects phase lag and amplitude for all frequencies using a measured transfer function for each tube.

In contrast to the low reduced frequencies for blade flitter, in the case of forced response, higher frequencies associated with higher order modes can be excited. Even for the low modes of blade flitter applications, higher fbw ve­locities at more realistic conditions require high physical frequencies to reach realistic reduced frequencies. If off-board pressure transducers are used to measure unsteady signals, these signals will be distorted by the pressure mea­surement system, and a correction must be performed. In the present paper, a tubing transfer function approach involving a frequency domain correction is described, typical transfer functions are presented, and the correction tech­nique is demonstrated for the tubing system in isolation, for surface pressures in a turbomachinery blade flutter case, and for wake measurements for a vortex shedding case.

DPIV plots of median velocity at the far spacing configuration are shown in Fig. 5. Due to the limit in laser sheet width, the flow field was not captured near the wake generator trailing edge. The wake shedding frequency is not easily determined as it was at close spacing. Hot wire measurements obtained downstream of the wake generator show the blade-pass frequency of 7.7 kHz

wake generator. An observation made from the instantaneous fbw visualiza­tion images (not presented here) suggest a phase locking of the wake shedding to the bow wave perturbation but random motion of the vortices as they con – vect downstream. At far spacing, two or three shed vortices are present at any given time in the gap between the wake generator and rotor. At close spacing, there is only one vortex present. As a result the averaged instantaneous images at far spacing do not show as clear a view of the wake region as close spacing. Nevertheless, plots of median velocity still illustrate important details of the far spacing ft>wfield.

Analysis of Fig. 5 shows bands of low and high velocity in the ft>w field that are a result of the rotor bow shock and expansion zone. At far spacing, the rotor bow shock is not as well defined because it is weaker than at close spacing. This is evident from the peak velocity magnitude observed in the DPIV images. The peak velocity at far spacing is approximately 220 m/s while at close spacing it is 245 m/s. Due to the increased axial gap between the rotor leading edge and wake generator the rotor bow shock has dissipated into more of a bow wave at the location it interacts with the wake generator trailing edge.

The wake generator wake has mixed out more resulting in a wider and shal­lower wake. The interaction of a weaker wake with a weaker bow shock does not split the rotor bow shock into two clearly defined regions such as was ob­served at close spacing.

3. Summary

A DPIV system for use in transonic turbomachinery has been described. Re­sults from an experiment conducted in the SMI rig are presented that show the complex flow field associated with the interaction of a downstream transonic rotor with an upstream stator. The effect of changing the axial gap between blade-rows is studied and the DPIV plots are presented as an experimental data set for time accurate CFD validation.

At close spacing, the wake shedding is synchronized with the rotor blade – pass frequency. The interaction of the rotor bow shock and wake generator causes the wake to expand downstream of the shock. The shock is split into two regions above and below the wake. As the shock approaches the wake gen­erator trailing edge, the velocity increases and the shock to turn more normal to the freestream flow.

At far spacing the wake convects downstream in a chaotic fashion. Bands of high and low velocity are evident from the rotor bow shock and expansion waves downstream of the shock. The interaction between the rotor bow shock and wake generator is much weaker than the close spacing interaction. The wake has mixed out more at the location it interacts with the shock and does not split the shock in two nor turn the shock normal to the freestream flow.

Acknowledgments

The wake generators, rotor, and stator were built by Pratt & Whitney. From the CARL group at Wright-Patterson AFB the authors would like to recognize Dr. Herb Law, Robert Wirrig, Ron Berger, Terry Norris, Bill Ullman, and Chris Blackwell for their assistance in gathering the data. The assistance of Dr. Sivaram Gogineni and Dr. Larry Goss of ISSI in setting up the DPIV system is also recognized. Post processing of the results was assisted by Justen England and Nathan Woods. The authors thank the Propulsion Directorate management for supporting the research and allowing the presentation and publication of this paper.

References

Sanders, A. and Fleeter, S. Experimental Investigation of Rotor-Inlet Guide Vane Inter­actions in Transonic Axial-Flow Compressor. AIAA Journal of Propulsion and Power, 16(3):421-430, 2000.

Smith, L. H. Wake Dispersion in Turbomachines. ASME Journal of Basic Engineering,

:668-690, 1966.

Smith, L. H. Wake Ingestion Propulsion Benefit. AIAA Journal of Propulsion and Power, 9(1):74—82, 1993.

Van Zante, D. E., Adamczyk, J. J., Strazisar, A. J., and Okiishi, T. H. Wake Recovery Per­formance Benefit in a High-Speed Axial Compressor. ASME Journal of Turbomachinery, 124:275-284, 2002.

Van de Wall, A. G., Kadambi, J. R., and Adamczyk, J. J. A Transport Model for the Deterministic Stresses Associated With Turbomachinery Blade Row Interactions. ASME Journal of Turbomachinery, 122:593-603, 2000.

Gorrell, S. E, Okiishi, T. H., and Copenhaver, W. W. Stator-Rotor Interactions in a Tran­sonic Compressor, Part 1: Effect of Blade-Row Spacing on Performance. ASME Journal of Turbomachinery, 125:328-335, 2003.

Gorrell, S. E, Okiishi, T. H., and Copenhaver, W. W. Stator-Rotor Interactions in a Tran­sonic Compressor, Part 2: Description of a Loss Producing Mechanism. ASME Journal of Turbomachinery, 125:336-345, 2003.

Strazisar, A. J. Investigation of Flow Phenomena in a Transonic Fan Rotor Using Laser Anemometry. ASME Journal of Engineering for Gas Turbines and Power, 107:427^35, 1985.

Ottavy, X., Trebinjac, I., and Voullarmet, A. Analysis of the Interrow Flow Field Within a Transonic Axial Compressor: Part 1 – Experimental Investigation. ASME Journal of Turbomachinery, 123:49-56, 2001.

Ottavy, X., Trebinjac, I., and Voullarmet, A. Analysis of the Interrow Flow Field Within a Transonic Axial Compressor: Part 2 – Unsteady Flow Analysis. ASME Journal of Tur­bomachinery, 123:57-63, 2001.

Calvert, W. J. Detailed Flow Measurement and Predictions for a Three-Stage Transonic Fan. ASME Journal of Turbomachinery, 116:298-305, 1994.

Law, C. H. and Wennerstrom, A. J. Two Axial Compressor Designs for a Stage Matching Investigation. Technical Report AFWAL-TR-89-2005, Air Force Wright Aeronautical Laboratory, WPAFB, OH, 1989.

Creason, T. and Baghdadi, S. Design and Test of a Low Aspect Ratio Fan Stage. AIAA Paper 88-2816, 1988.

Gorrell, S. E., Copenhaver, W. W., and Chriss, R. M. Upstream Wake Infliences on the Measured Performance of a Transonic Compressor Stage. AIAA Journal of Propulsion and Power, 17(1):43-48, 2001.

[1] Gorrell, S. E. An Experimental and Numerical Investigation of Stator-Rotor Interactions in a Transonic Compressor. PhD thesis, Iowa State State University, Ames, Iowa, 2001.

Chriss, R. M, Copenhaver, W. W., and Gorrell, S. E. The Effects of Blade-Row Spacing on the Flow Capacity of a Transonic Rotor. ASME Paper 99-GT-209, 1999.

Estevadeordal, J., Gogineni, S., Goss, L., Copenhaver, W., and Gorrell, S. Study of Wake-Blade Interactions in a Transonic Compressor Using Flow Visualization and DPIV. ASME Journal of Fluids Engineering, 124(1): 166-175, 2002.

Copenhaver, W., Estevadeordal, J., Gogineni, S., Gorrell, S., and Goss, L. DPIV study of near-stall wake-rotor interactions in a transonic compressor. Experiments in Fluids, 33:899-908, 2002.

Hart, R. The Elimination of Correlation Errors in PIV Processing. In 9th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 1998.

Westerweel, J. Fundamentals of Digital Particle Imaging Velocimetry. Measurement Sci­ence and Technology, 8:1379-1392, 1997.

J., Estevadeordal, Gogineni, S., Goss, L., Copenhaver, W., and Gorrell, S. DPIV Study of Wake-Rotor Synchronization in a Transonic Compressor. AIAA Paper 01-3095, 2001.

DPIV results are presented for close and far spacing configurations at 75% span, 100% corrected speed, peak efficiency. Of particular interest is the in­teraction between the wake generator wake and the rotor bow shock and the effect blade-row axial spacing has on the overall flow field. The median of 50 instantaneous images is plotted as it was found that it provided the clearest image of the flow field.

2.1 Close Spacing

Previous analysis of fbw visualization and DPIV results from the SMI rig (Refs. [17], [18], and [21]) have shown that at close spacing vortex shedding from the wake generator trailing edge is phase locked to the rotor blade pass frequency. The main source of the synchronization appears to be the strong pressure perturbation provided by the rotor bow shock to the wake generator trailing edge. At close spacing the instantaneous images of vortex shedding are similar for any given operating condition and blade delay. This is consistent with high response pressure measurements obtained on the wake generator sur­face, which showed a strong fhctuation in pressure at blade-passing frequency (7.7 kHz). Since the instantaneous DPIV data contains holes in velocity in­formation where seeding was not sufficient to obtain a correlation, it is more informative to look at the average fbw field where data intermittency can be minimized. Since the vortex shedding is phase locked to rotor passing, rotor phase locked averaging is possible without destroying the details of the veloc­ity field in this interaction region.

At close spacing DPIV measurements were made at blade delay intervals of 5 3ts giving 30 different rotor blade locations for one blade-pass period. Seven of the blade delays are shown in Fig. 5. The rotor bow shock is defined by the large velocity gradient and a change in fbw angle toward the shock. Stream­lines are drawn near the wake generator to highlight the wake motion at differ­ent rotor locations. The wavy motion of the wake is a result of a vortex being shed from the pressure or suction surface of the wake generator. This up and down motion continues as the wake convects downstream and interacts with the rotor bow shock and then is chopped by the rotor blade. Downstream of the rotor bow shock there is an expansion zone due to the ft>w accelerating around the rotor suction surface.

The DPIV images at blade delay 140 ^s and 20 ^s illustrates that the shock – wake interaction results in a wider and deeper wake downstream of the shock. At time 20 ^s the low velocity region downstream of the shock and within the wake moves up to 18% pitch suggesting that the shock-wake interaction has resulted in an increase in wake width.

From the plot at blade delay 140 ^s it is clear that the wake actually splits the shock into two distinct regions above and below the wake. It was also observed that the velocity magnitude at the wake generator trailing edge flic – tuates significantly depending on the location of the rotor bow shock. As the shock approaches the wake generator the velocity increases first near the wake generator pressure surface, then on the suction surface. Once the shock is sep­arated and propagates upstream the velocity magnitude decreases. Numerical analysis reported by Gorrell et al. [7] showed that the interaction of the wake generator trailing edge with the rotor bow shock causes the shock to turn more normal to the freestream flow. This phenomenon is also observed in the exper­imental data presented in Fig. 5.

Performance characteristics for the SMI rig are shown in Fig. 5. There was a significant difference in performance between each of the three spacings tested. Both the pressure ratio and efficiency characteristics decreased significantly as the blade-row axial spacing was reduced from far to close. The choking mass fbw rate decreased as the blade-row axial spacing was reduced. The difference in pressure ratio, efficiency, and mass fbw rate between the far and close spac­ing configurations was greater than the repeatability documented in Ref. [14]. Therefore it was concluded that the observed change in performance with axial blade-row spacing was real and not due to experimental measurement uncer­tainty.

2. DPIV System

The DPIV system used to obtain the measurements presented in this paper has been described in detail by Estevadeordal et al. [17]. Figure 5 contains schematics of the optical system. Two frequency-doubled Nd:YAG lasers are employed for instantaneous marking of the seed particles in the flow field. Combined by a polarizing cube or a beam combiner, the beams are directed through sheet-forming optics and illuminate the test section with a 2D plane of thickness ~1 mm. The scattering from the seed particles is recorded on a cross­correlation CCD camera with 1008 x 1018 pixels (Redlake ES1.0). The camera maximum repetition rate is 15 double exposures per second and was set to 10 Hz for synchronization with the laser repetition rate. The time delay between

the lasers was typically 2 ^sec. For the present experiments where only a small area was to be captured, the camera offered sufficient resolution. A 105­mm Nikon lens was used. The magnification for the present experiments was 17 and 27 pixels/mm which corresponds to a viewing width of 59 mm (close spacing) and 37 mm (far spacing).

The laser-sheet delivery system consists of a probe inserted in an enlarged WG, light-sheet-forming optics, prisms, and probe holders for mounting the optics and for protecting them from contaminated seed materials. To mini­mize perturbations the modified WG was located two WGs below the WG that was centered at the receiving window. A receiving window made of chemi­cally strengthened glass allowed optical access to the region of interest. Fig­ure 5 shows schematic diagrams of the path for the laser system and the optical probe. Although the path was relatively long, the power required for laser-sheet

illumination was very low (~10 mJ/pulse) because of the minimal amount of optics loses. The F stop of the 105 mm lenses was kept at 5.6 for these ex­periments; this allowed the laser power to be kept low which is important for the safety of the optical components in the optical probe as the beam starts focusing.

The shape of the laser sheet (thickness, width, focal distance) can be changed through various combinations of the spherical-lens focal length, the cylindrical – lens diameter, and the distance between them inside the WG as well as through external optics (a spherical lens) located in the laser path. The spanwise loca-

The length of the probe that was outside the WG could also be changed to provide further flexibility in moving the laser-sheet in the streamwise direction. The probe was set manually before each experiment.

The camera was aligned and focused on the laser sheet prior to each run. It was mounted on a tripod to minimize the effect of rig vibrations. To account for possible motion of the camera with respect to the laser sheet that might occur, the camera was positioned by means of a translation stage that was remotely controlled to allow small corrections in the camera location. Large changes with respect to the laser sheet could produce magnification changes that must
be taken into account. After every experiment, the laser-sheet and camera locations were verified for possible misplacements. In the present experiments, the only change required was slight refocusing, with negligible magnification effects.

The viewing window had the same curvature as the rotor housing (inner housing radius is 241.3 mm), was made of chemically strengthened glass, and had a thickness of 2 mm. The effect of window curvature and thickness was investigated by Copenhaver et al. [18] and found to have a negligible effect for the present CARL setup.

Several options for seeding the high-fhw (~ 16 kg/s) SMI rig in the CARL facility were evaluated [17], including the use of various seeding units and seed materials. Both local and global seeding was considered. The seed material used was sub-micron-size smoke particles generated from a glycerin and water mixture. During its use in the CARL facility, this system produced sufficient seed when the particles were introduced at the end of the settling chamber, before the contraction, and at the height of the receiving window. The machine can be remotely controlled. The seed material was introduced through a pipe of 50.4-mm diameter located under the contraction entrance.

The rotor one-per-revolution signal was used for triggering the synchroniza­tion system. A digital pulse generator (Stanford DG535) and a camera frame – grabber (National Instruments PCI-1424) were used.

Once the PIV images have been captured and digitized, the velocity field is obtained using cross-correlation techniques over interrogation domains of the images using DPIV software developed internally. The dimensions of each in­terrogation domain are dependent on particle density, estimated local velocity gradients, particle-image size, and desired spatial resolution. The peak of the correlation map corresponds to the average velocity displacement within the interrogation spot. An intensity-weighted peak-searching routine is used to de­termine the location of the peak to sub-pixel accuracy. To improve the signal – to-noise ratio in the correlation maps, a correlation-correction scheme [19] is applied wherein each map is multiplied by its immediate four neighborhoods. An overlapping of 75% is used to include much the same particles in the five maps that are multiplied to yield a single correlation map with lower noise. Zero padding is also employed for adding accuracy. The software includes a grid feature that allows selection of areas of the image to be processed. This permits removal of solid regions such as blades and WGs and also shadows from the processing areas. It also provides a choice of various correlation en­gines and correlation peak locators and incorporates several improvements to standard (single-pass) PIV techniques such as recursive estimation of the ve­locity field through a multipass algorithm for increasing resolution. Two passes with interrogation cells overlapping 75% were performed. The interrogation domains are overlapped by three-quarters the domain size to yield more vec­tors. The overlapping includes new particles in every subregion. Average rou­tines allow for removal of outliers beyond any number of standard deviations. Because of the strong phase-locked ft>w features, the median offers a valid, robust, and smooth statistical representation of the average velocity field [17].

Many factors are involved in the DPIV uncertainty-calculation process (laser, CCD, seeding, imaging, algorithms, oscilloscope, etc.). The highest uncer­tainty was found to be associated with the velocity calculation which involves Ax (the displacement in pixels of each interrogation region), At (the time in­terval between the two exposures), and the magnification of the digital image relative to the object (pix/m). The displacement in pixels obtained by peak – locator algorithms can provide sub-pixel accuracy (< 0.1 pixels) after correc­tion for various biases [20]. The At was adjusted to yield typical displacements of the main stream > 10 pixels, and the uncertainty is thus <1%. Values in the wake region, however, may have higher uncertainties due to the lower Ax. The maximum uncertainty in the At was calculated from the time interval between the two laser pulses with the aid of an oscilloscope (uncertainty 2%). It was found that this uncertainty increases with lower laser power and with lower At. A conservative number for the present experiments, which employed a At of about 2 ps and powers around 10 mJ, was found to be 1%. The magnification was measured using images of grids located in the laser-sheet plane to better than 1%. Combining these conservative measurements of uncertainty yields a maximum error of < 2% for the free-stream velocity and ~10% in the wake near the WG area.

The DPIV measurements were acquired on the U. S. Air Force’s Stage Matching Investigation (SMI) rig. It is a high-speed, highly-loaded compres­sor consisting of three blade-rows: a wake generator, rotor, and stator as shown in Fig. 5. The rig was designed so that the wake generator to rotor axial spac­ing and the wake generator blade count could be varied. The axial spacings were denoted as "close", "mid", and "far". The mid and far spacings repre­sent typical axial gaps found in operational fans and compressors. However, the current generation of high performance fans and compressors are being designed with the goal of minimizing blade-row spacing in order to increase performance and reduce compressor length and thus weight. The wake genera­tor blade count could be set to 12, 24, or 40, or the rig could be run without any wake generators (identified as the "clean inlet" configuration). Table 1 gives the wake generator to rotor axial spacings normalized by the wake generator chord.

1.1 Compressor Stage and Wake Generators

The rotor and stator were designed by Law and Wennerstrom [12]. A sum­mary of the SMI stage aerodynamic design parameters is given in Table 2. The purpose of the wake generators was to create wakes typically found in modern-technology, highly-loaded, low-aspect-ratio fan and compressor front stages. In general, these wakes are turbulent and do not decay as rapidly as

Table 1. Wake Generator-Rotor Axial Spacing

Spacing ax/c ax/c ax/c (tip)

Close 0.13 0.10 0.14

Mid 0.26 0.26 0.26

Far 0,55 0.60 0.52

ax = axial spacing c = wake generator chord

wakes from high-aspect-ratio stages with lower loading. The wake generators were designed with the intent of producing a two-dimensional representation of wakes measured at the exit of a high-pressure-ratio, low-aspect-ratio fan stage reported by Creason and Baghdadi [13]. A two-dimensional represen­tation was desired in order to isolate the effect of different wake parameters during the experiment.

Details of the Wake Generator (WG) design were presented by Gorrell et al. [14]. In summary, the WG’s are uncambered symmetric airfoils that do not turn the ft>w. They have a small leading edge and a blunt trailing edge. This shape creates a large base drag and no swirl. Solidity is held constant from hub to tip by varying the chord, the intent being to hold spanwise loss and wake width constant.

Calibration of the WG’s showed this was the case except near the end – walls. The calibration procedure, instrumentation, and results are found in

Refs. [15] and [16]. From those results, the widening of the wake from close to far spacing was clearly evident. Wake depth was deepest at close spacing and became shallower at mid and far spacing. The wake width was nearly constant from hub to case. This confirmed the intent of the wake generator design to produce a two-dimensional wake profile. The wake is constant in the circum­ferential and radial directions but not in the streamwise direction. Also evident from rake measurements near the endwalls was the boundary layer growth as the spacing increased from close to far.

From calculated velocity profiles, it was observed that the wake depth was similar at the hub and case and deepest near mid span. Wake decay analyzed by Chriss et al. [16] showed that the SMI wake generator wakes demonstrated similar trends to that compared in the literature.

Due to the blunt trailing edge of the wake generator, its wakes may be wider than what would be produced from a normally cambered stator airfoil, but wake measurements for comparison are not found in the open literature. Re­gardless of the wake thickness, the loss produced was very near the design intent and well within the range typically found in highly loaded stators.

Steven E. Gorrell, William W. Copenhaver U. S. Air Force Research Lab Propulsion Directorate Wright-Patterson AFB, Ohio

Jordi Estevadeordal

Innovative Scientific Solutions, Inc.

Beavercreek, Ohio

1. Introduction

The use of a planar non-intrusive measurement techniques such as Digital Particle Image Velocimetry (DPIV) have made it possible to investigate many aspects of unsteady fbws previously considered difficult due to the effect of a measurement probe on the fbw field, or too time consuming because of the pointwise nature of Laser Doppler Velocimetry or Laser Transit Anemometry. Furthermore, time-accurate CFD codes are being developed and are now com­monly used to simulate compressors and investigate complex unsteady fbw phenomenon.

In this paper, DPIV measurements made in a transonic compressor stage are used to investigate interactions between an upstream stator and a downstream transonic rotor. In particular, the interaction between the rotor bow shock and the wake shed from the upstream stator are explored and offered as a test case for unsteady CFD comparison.

Blade-row interactions are known to have a significant impact on the aerome – chanical and aerodynamic performance of compressors. For example, Sanders and Fleeter [1] have shown shock-induced rearward forcing to elicit significant upstream surface-pressure amplitudes and a complicated forcing environment that contributes to High Cycle Fatigue (HCF). Numerous low speed and high speed experimental and numerical investigations [2], [3], [4], [5], [6], [7] have revealed how some blade row interactions improve stage pressure ratio and efficiency while others are detrimental to performance.

505

K. C. Hall et al. (eds.),

Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 505-519. © 2006 Springer. Printed in the Netherlands.

Previous experiments using pointwise velocimetry techniques have been used to better understand the three-dimensional geometry of rotor shocks [8], wake recovery [4], wake-shock interactions [9], [10], and for steady CFD code comparison [11].

The measured pressure spectra at the diffuser outlet are presented in Fig. 7. The results from different operation points and different circumferential an­gles are shown. At the operation point near the surge, the largest amplitude of the pressure variation is seen at the circumferential angle 348 °. However, the largest amplitude of the pressure variation at the diffuser inlet is seen at the circumferential angle 168° (see Fig. 5). There is no large amplitude of pressure variation at the blade passing frequency at the diffuser outlet. On the other hand, pressure variations at the blade passing frequency are visible at the diffuser inlet.

At the design operation point the largest amplitude of the pressure variation is seen at the frequency of every second blade (see Fig. 7). This is also seen at the diffuser inlet, but the amplitude is larger.

At the operation point near the choke the largest amplitude of the pressure variation is seen at the frequency of every second blade and at the circumfer­ential angle 168°. This is also seen at the diffuser inlet.

The calculated pressure spectra are presented in Fig. 8. The results from the design operation point, the operation point near the choke and different circum­
ferential angles are shown. The pressure variation can be seen at the passing frequency of every second blade at the design operation point. The amplitude of the pressure variation decreases when the circumferential angle increases. The magnitude of the pressure variation in the measured data is equal to the magnitude of the pressure variation in the calculated data at the circumferential angles 168° and 348°. Small amplitude of the pressure variation is also seen both in the measured and in the calculated data at the blade passing frequency.

At the operation point near the choke, the behavior of the pressure is similar to the behavior of the pressure at the diffuser inlet. Only the amplitude of the pressure variations is smaller. The calculated data shows large amplitude pres­sure variations at the frequency of every second blade at the circumferential angles 78° and 348°, which are not seen in the measured pressure spectra.

5. Conclusions

An unsteady fbw field in the vaneless diffuser of a centrifugal compres­sor was investigated. Unsteady static pressure was measured at the diffuser inlet and outlet at different circumferential angles. A time-accurate numer-

ical simulation was conducted to the tested compressor. A FFT was made to the measured and calculated static pressure. The provided pressure spectra were analyzed, and the measured and calculated data were compared with each other.

It can be concluded that most of the pressure variations lay at the passing frequency of every second blade. Pressure variations did not vanish in the diffuser and were visible at the diffuser outlet. However, the amplitude of the pressure variations decreased in the diffuser. It can be also concluded that the measured pressure variations were largest at the design operation point.

The time-accurate calculations showed quite good agreement with the mea­sured data. Agreement was very good at the design operation point, even though the computational grid was not dense enough in the volute and exit cone. The time-accurate calculation over-predicted the amplitude of the pres­sure variations in the operation point near the choke.

Acknowledgments

The authors wish to thank the National Technology Agency (TEKES), High Speed Tech Oy Ltd and Sundyne Corporation for financing this research. CSC – Scientific Computing Ltd provided the computer resources for the numerical work. The authors also wish to thank the Laboratory of Applied Thermody­namics at Helsinki University of Technology and Finfb Oy Ltd for their kind cooperation.

References

Fatsis, A., Pierret, S., Van den Braembussche, R. (1997). Three-Dimensional Unsteady Flow and Forces in Centrifugal Impellers with Circumferential Distortion of the Outlet Static Pressure. Journal of Turbomachinery, Vol. 119, pp. 94-102.

Hillewaert, K., Van den Braembussche, R., A. (1999). Numerical Simulation of Impeller – Volute Interaction in Centrifugal Compressors. Journal of Turbomachinery, Vol 121, pp. 603-608.

Koumoutsos, A., Tourlidakis, A., Elder, R., I. (2000). Computational Studies of Unsteady Flows in a Centrifugal Compressor Stage. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, Vol. 214, No. 6, pp 611-633.

Rai, M. (1986). A Relaxation Approach to Patched.-Grid Calculations with the Euler Equations. Journal of Computational Physics, Vol. 66, No. 1, pp 99-131.

Chien, K. (1982). Predictions of Channel and Boundary-Layer Flows with a Low – Reynolds-Number Turbulence Model. AIAA Journal, Vol. 20, No 1. pp 33-38.

Reunanen, A. (2001). Experimental and Numerical Analysis of Different Volutes in a Centrifugal Compressor. Lappeenranta, Lappeenranta University of Technology, Acta Universitatis Lappenrantaensis 118. Diss.

Siikonen, T., Pan, H. (1992). An Application of RoeSs Method for the Simulation of Viscous Flow in Turbomachinery. In: Hirch et al. (eds) Computational Fluid Dynamics ’92, Vol.2, Proceeding of the First European Computational Fluid Dynamics Conference, Brussels, Sept. 7-11, 1992. Elsevier Science Publishers B. V. pp. 635-641.

Siikonen, T. (1995). An Application of RoeSs Flux-Difference Splitting for the k — e Turbulence Model. International Journal for Numerical Methods in Fluids, Vol 21, pp. 1017-1039.

Message Passing Interface Forum. (1994). SMPI: A message-passing interface stan – dard. S, Technical Report CS-94-230, Computer Science Dept., University of Tennessee, Knoxville, TN.

Rautaheimo, P., Salminen, E., Siikonen, T. (1996). Parallelization of a Multi-Block Navier-Stokes Solver. In Proceedings of the ECCOMAS Congress, Paris, Sept.

Hoffren, J. (1992). Time-Accurate Schemes for a Multi-Block Navier-Stokes Solver. Re­port A-14, Helsinki University of Technology, Laboratory of Aerodynamics, ISBN 951­22-1350-8.

The measured pressure spectra at the diffuser inlet are presented in Fig. 5. The results from different operation points and different circumferential angles are shown. At the operation point near the surge, one can see small variation of the pressure at the blade passing frequency (about 5050 Hz) at every cir­cumferential angle. The amplitude of the pressure variation is about 200 Pa. At the circumferential angle 168° and 348° one can also see the pressure vari­ations at the frequency of every second blade (about 2525 Hz). The amplitude of the pressure variation is larger at the circumferential angle 168 ° than at the circumferential angle 348°.

At the design operation point, the amplitude of the pressure variations are largest at the frequency of every second blade. The amplitude is a little bit larger at the circumferential angle 168° than at the other circumferential angles. No clear pressure variation is seen at the blade passing frequency.

At the operation point near the choke, larger amplitude of the pressure vari­ations is seen at the circumferential angle 168°. The frequencies of the vari­ations are the blade passing frequency and the frequency of the every other blade. The larger pressure variation is also seen at the circumferential an­gle 348°, and at the blade passing frequency. One can also notice that there are smaller pressure flictuations at the multiplex frequencies of the rotational speed at every operation point. These flictuations get larger when the ft>w through the compressor is increased (see Fig. 5).

The calculated pressure spectra are presented in Fig. 6. The results from the design operation point, the operation point near the choke, and the different cir­cumferential angles are shown. At the design operation point, one can clearly see pressure variation at the blade passing frequency and at the frequency of every second blade. The amplitude of the pressure variation is largest at the circumferential angle 168° and at the frequency of every second blade. The magnitude of the amplitude is the same in the measured and in the calculated pressure spectrum at the frequency of every second blade. On the other hand,
pressure variation is not seen in the measured spectrum at the blade passing frequency (see Fig. 5).

There are larger pressure variations at the multiplex frequency of the rota­tion speed at the operation point near the choke. The largest amplitude of the pressure variations is seen at the frequency of every second blade and at the circumferential angles 78° and 348°. These are not seen in the measured pres­sure spectra (see Fig. 5). Larger amplitude of pressure variations is also seen at the blade passing frequency in the calculated spectra. This is also seen in the measured spectra at the circumferential angles 168° and 348°.

The measured data was collected with the measuring frequency of 1 MHz. 30000 data points were collected, which is a 0.03 s period of time. This is 10.8 rotations of the impeller. Three measurements were made at each measuring point and at each operation condition. The measured data was phase averaged over ten rotations of the impeller, and three different sets of measured data were compared to each other to ensure the regularity of the achieved pressure variations. In this case, phase averaging means that the 10 impeller rotations-

long measured data were cut in ten 1-rotation-long pieces with the help of the measured rotation speed. Then the measured pressure data points at the same position of the impeller were averaged. The fast Fourier transform (FFT) was made to examine pressure flictuations in the frequency plane.

The time step used in the computational calculations was 1^s. 11600 time steps were calculated, which is about four rotations of the impeller. The data was collected from the last full rotation of the impeller. The data was taken only at every 10th time step. Even when the data was collected from the last rotation of the impeller and from every 10th time step, the amount of achieved data was over 5 Gb. Static pressures were collected from the calculated data at the same location where the measurements were made. A FFT was also made for the calculated data.

4. Results

The computational grid of the compressor is divided to 33 blocks and the number of the computational cells is 618,496. The surface grid of the com­pressor is shown in Fig. 3. Every second grid line is visible. Tip clearance is not modeled. The topology of the grid has been made in such way that the all blocks except the ones in the volute and exit cone contain clustering near to the walls (Fig. 4).

The infbw boundary conditions for the numerical simulation are given at beginning of the inlet pipe, which is located 1.05 meters above the impeller leading edge. Total enthalpy, mass flow and flow direction at the inlet are defined. The pressure is extrapolated from the fbw field and the density is iterated with the help of the total enthalpy and the pressure. The velocity dis­tribution is uniform and the intensity of the turbulence and the dimensionless turbulent viscosity are defined at the inlet plane. The distributions of the veloc­ity and the quantities of the turbulence start to develop before the leading edge of the impeller since the inlet pipe is long. The outflow boundary conditions are given at the end of the outlet pipe 1.60 meters downstream of the end of the volute. The static pressure is given at the outlet to define the pressure level of the solution.

The numerical solver Finfb has been used to carry out the simulations. Finfb is a Navier-Stokes solver developed at Helsinki University of Technol­ogy. The Reynolds averaged Navier-Stokes equations are solved by a Finite – Volume method. The code utilizes Roe’s Flux-difference splitting, and con­vergence is accelerated by a multigrid method. More details can be found in Refs. [7] and [8]. The parallelization of the code is based on the Message Passing Interface (MPI) standard [9]. The computational domain is divided into groups of blocks and the boundaries between the groups are updated us­ing MPI. The number of cells in the groups should be equal in order to get the

best benefit from the parallelization. On the other hand, the different groups can contain different amounts of block, which makes it easy to assign the same number of grid cells to each processor to ensure an equal division of the com­putational workload. [10]. Time-accurate simulation is based on a three-level fully implicit second order time-integration method. This method is described in [11]. The inner iterations are made at every time step. The number of the inner iterations is chosen to get convergence for each time step. In our case, 25 seems to be enough. In this case, the time step is 1^s, which has been found to be small enough to get a solution. The rotor of the compressor is rotated 0.13 ° at every time step. The connection between the stationary and the rotating part of the mesh is handled by using a sliding mesh technique. The grid lines be­tween the impeller blocks and the stator block are discontinuous, thus a mass conserving interpolation is made at every time step.

The experiments were conducted in the Laboratory of the Fluid Dynamics at Lappeenranta University of Technology. The layout of the test facility can be seen in Fig. 1. The test stand allows the measurement of ambient pressure, tem­perature and humidity, mass fbw, inlet total pressure and temperature, outlet total pressure and temperature, rotational speed and input power. The com­pressor can be monitored on-line with the help of an in-house developed data acquisition program.

The unsteady static pressure inside the vaneless diffuser was measured using Kulite XTC-190 miniature transducer. The pressure transducer is mounted to the shroud wall in the diffuser inlet and to the hub wall in the diffuser outlet. The unsteady pressure was also measured at three different circumferential angles 78°, 168° and 348° in the diffuser inlet and outlet (see Fig. 2).

Ami ;-n’ temperature.

pressure and hunurutv

Flow stiarghtener

Inlet temperature

Outlet

[■ mam

Electnc

power

Figure 1. The compressor test facility